Issue: Path Parameter Extraction for Complex Google API Endpoints

[goldylocks87]

Describe the bug
The Google API tool converter uses the _extract_path_parameters method to extract string parameters. It fails to parse path parameters in endpoint patterns like /v1/documents/{documentId}:batchUpdate. The method looks for URL segments that start with { and end with }, but in patterns like {documentId}:batchUpdate, the segment ends with :batchUpdate, not }, causing the parameter extraction to fail.

Error received in UI:

{"error": "'documentId'"} 

Error in terminal:

\google\adk\tools\openapi_tool\openapi_spec_parser\rest_api_tool.py", line 283, in _prepare_request_params
    url = f"{base_url}{self.endpoint.path.format(**path_params)}"
                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
KeyError: 'documentId'
2025-07-07 00:23:22,901 - ERROR - __init__.py:157 - Failed to detach context

To Reproduce
Steps to reproduce the behavior:

1. Enable the Google Docs & Vertex APIs in Cloud Console
2. Create OAuth credentials (use type Desktop)
3. Create a basic ADK Agent (see below)
4. Open the playground (make playground)
5. Ask the agent to create a doc
6. Authenticate
7. Ask the agent to add text to the document

Repro Agent

import os

import google.auth
from google.adk.agents import Agent
from google.adk.tools.google_api_tool import DocsToolset
from googleapiclient.errors import HttpError

try:
    _, project_id = google.auth.default()
    os.environ.setdefault("GOOGLE_CLOUD_PROJECT", project_id)
    os.environ.setdefault("GOOGLE_CLOUD_LOCATION", "global")
    os.environ.setdefault("GOOGLE_GENAI_USE_VERTEXAI", "True")

    # Validate environment variables
    if not os.getenv("GOOGLE_OAUTH_CLIENT_ID") or not os.getenv("GOOGLE_OAUTH_CLIENT_SECRET"):
        raise ValueError("GOOGLE_OAUTH_CLIENT_ID and GOOGLE_OAUTH_CLIENT_SECRET must be set")

    docs_toolset = DocsToolset(
        client_id=os.getenv("GOOGLE_OAUTH_CLIENT_ID"),
        client_secret=os.getenv("GOOGLE_OAUTH_CLIENT_SECRET")
    )

    # Create the agent with Google Docs tools
    root_agent = Agent(
        name="root_agent",
        model="gemini-2.0-flash",
        instruction="You are a helpful AI assistant designed to use the good docs tool to create a documents.",
        tools=[docs_toolset],  # Pass as a list containing the toolset
    )
except Exception as e:
    print(f"Error type: {type(e)}")
    print(f"Error args: {e.args}")
    print(f"Error dict: {e.__dict__}")
    raise

Expected behavior
Agents should be able to call the batchUpdate API in the Google Document spec

Desktop (please complete the following information):

• OS: Windows
• Python version(python -V): Python 3.12.4
• ADK version(pip show google-adk): 1.5.0

Model Information:
gemini-2.0-flash

Additional context
Assuming the location parameter is correctly documented in the discovery apis, that could be used instead of extracting directly from the url string.